Slow wake recovery and low turbulence behind wind farms parameterized in mesoscale simulations

Radünz, William C.; Kasper, Jens H.; Stevens, Richard J. A. M.; Lundquist, Julie K.

doi:10.5194/wes-11-2723-2026

Articles | Volume 11, issue 7

https://doi.org/10.5194/wes-11-2723-2026

© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/wes-11-2723-2026

© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 11, issue 7

Research article

|

30 Jul 2026

Research article |

| 30 Jul 2026

Slow wake recovery and low turbulence behind wind farms parameterized in mesoscale simulations

William C. Radünz, Jens H. Kasper, Richard J. A. M. Stevens, and Julie K. Lundquist

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Final revised paper (published on 30 Jul 2026)
Preprint (discussion started on 08 Sep 2025)

Interactive discussion

Status: closed

RC1: 'Comment on wes-2025-147', Anonymous Referee #1, 24 Sep 2025

see supplement

Citation: https://doi.org/10.5194/wes-2025-147-RC1
RC2: 'Comment on wes-2025-147', Anonymous Referee #2, 06 Oct 2025

See attachment

Citation: https://doi.org/10.5194/wes-2025-147-RC2
RC3: 'Comment on wes-2025-147', Anonymous Referee #3, 07 Nov 2025

The comment was uploaded in the form of a supplement: https://wes.copernicus.org/preprints/wes-2025-147/wes-2025-147-RC3-supplement.pdf

Citation: https://doi.org/10.5194/wes-2025-147-RC3
AC1: 'Comment on wes-2025-147', William C. Radünz, 23 Jan 2026

The comment was uploaded in the form of a supplement: https://wes.copernicus.org/preprints/wes-2025-147/wes-2025-147-AC1-supplement.pdf

Citation: https://doi.org/10.5194/wes-2025-147-AC1

Peer review completion

AR – Author's response | RR – Referee report | ED – Editor decision | EF – Editorial file upload

AR by William C. Radünz on behalf of the Authors (26 Jan 2026) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (27 Jan 2026) by Alfredo Peña

RR by Anonymous Referee #2 (03 Mar 2026)

Suggestions for revision or reasons for rejection

The authors are praised for conducting additional simulations and rephrasing several of the previous exaggerated statements. The manuscript has improved significantly.

The fundamental issue remains about the term “under-resolved gradient”. The authors insist that this interpretation of their results is correct, but, as also another reviewer pointed out and as I discuss further below, this term is misleading and inaccurate and therefore it should be removed from the manuscript. The title could be changed to simply: “Slow wake recovery and low turbulence behind wind farms parameterized in mesoscale simulations”. Any use of, or reference to, the term or concept of “under-resolved gradients” must be eliminated if the manuscript is to be considered for publication any further.

I bring forward three examples (from the reply) that illustrate that the concept of under-resolved gradients is bogus in the revised manuscript.

1. “[under-resolved gradients are] a feature that occurs mostly outside the grid cells where the WFP acts, downstream of the wind farm. “Under-resolved gradients” refer to how the wake behind a wind farm is represented in a mesoscale grid and the consequent impacts on wake recovery compared with the LES.”

The authors insist that the term is appropriate but now their new arguments become contradictory and inconsistent. This is the first time that they mention that the term “under-resolved gradients” refers to the grid cells OUTSIDE and DOWNSTREAM of the wind farm; this was never explained in the original paper. However, this re-definition now implies that under-resolved gradients do not occur and/or are not relevant in the grid cells INSIDE the wind farm, which is instead where the gradients are the most unresolved!

2. “We agree that when gradients are evaluated using WRF-scale differencing, locally large instantaneous gradients can occur in the mesoscale model, sometimes exceeding those diagnosed from the coarsened LES.”

I already pointed out in my previous review that their own results show that sometimes the gradients are actually over-resolved, not under-resolved, by the mesoscale model. The authors state that these cases are not “spatially coherent” and not “organized” and therefore do not generate enough turbulence via shear. This is not true because the patterns are actually well organized and the shear generation must be large in the presence of such strong resolved gradients. If the mesoscale model sometimes generates under-resolved gradients but sometimes it generates over-resolved gradients, it means that the concept of under-resolved gradients is not universal and not always applicable in the presence of a WFP.

3. “A potential path forward is the development of a subgrid model that accounts for the missing spatial gradients driving wake recovery.”

This is a troublesome recommendation, because, again, it implies that these under-resolved gradients are the problem to address, whereas they may be (at times) the consequence of the limitations of the WFPs. A sub-grid model should not try to generate sub-grid gradients, but sub-grid wakes. This is another example of how under-resolved gradients are treated as the cause of the problem, as opposed to a manifestation of one.

Bottom line: the very concept of under-resolved gradients is obscure and contradictory and should be removed from the manuscript.

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RR by Anonymous Referee #3 (27 Mar 2026)

ED: Reconsider after major revisions (30 Mar 2026) by Alfredo Peña

AR by William C. Radünz on behalf of the Authors (11 May 2026) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (12 May 2026) by Alfredo Peña

RR by Anonymous Referee #3 (16 Jun 2026)

RR by Anonymous Referee #2 (18 Jun 2026)

ED: Publish subject to minor revisions (review by editor) (19 Jun 2026) by Alfredo Peña

AR by William C. Radünz on behalf of the Authors (29 Jun 2026) Author's response Author's tracked changes Manuscript

ED: Publish as is (30 Jun 2026) by Alfredo Peña

ED: Publish as is (01 Jul 2026) by Sandrine Aubrun (Chief editor)

AR by William C. Radünz on behalf of the Authors (07 Jul 2026) Author's response Manuscript

Short summary

Wind farms extract energy from the wind, creating slower, more turbulent flows that can affect other farms downstream. Using high-fidelity simulations for comparison, we find that mesoscale simulations that parameterize wind farms at coarser resolution may underestimate how quickly the wind recovers downstream. This slow recovery results from missing sharp wind gradients and low turbulence. Improving these aspects can help better predict wind energy production over long distances.